Generalized non-associative structures on the 7-sphere
Abstract
In this paper we provide a more general class of non-associative products using the exterior and Clifford bundles on the 7-sphere. Some additional properties encompass previous formalisms in the Clifford algebra context, and wider classes of non-associative structures on the 7-sphere are investigated, evinced by the directional non-associative products and the mixed composition of generalized non-associative products between Clifford algebra multivectors. These non-associative products are further generalized by considering the non-associative shear of arbitrary Clifford bundle Cl(0,7) elements into octonions. We assert new properties inherited from the non-associative structure introduced in the whole Clifford bundle on S7, which naturally induce involutions on the Clifford bundle and provide immediate generalizations concerning well-established formal results and potential applications in physics.
Keywords
Cite
@article{arxiv.1109.0859,
title = {Generalized non-associative structures on the 7-sphere},
author = {Roldao da Rocha and M. A. Traesel},
journal= {arXiv preprint arXiv:1109.0859},
year = {2012}
}
Comments
36 pages, JPConf style